2a^2+3a+6a+9=

Solution for 2a^2+3a+6a+9= equation:

Simplifying
2a2 + 3a + 6a + 9 = 0

Reorder the terms:
9 + 3a + 6a + 2a2 = 0

Combine like terms: 3a + 6a = 9a
9 + 9a + 2a2 = 0

Solving
9 + 9a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + a)(3 + 2a) = 0

Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(3 + 2a)' equal to zero and attempt to solve:

Simplifying
3 + 2a = 0

Solving
3 + 2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2a = 0 + -3
2a = 0 + -3

Combine like terms: 0 + -3 = -3
2a = -3

Divide each side by '2'.
a = -1.5

Simplifying
a = -1.5
Solution
a = {-3, -1.5}